Abstract
We have measured the plasmon dispersion in polycrystalline Beryllium at wave vectors up tok=1.29 Å−1 with electron energy loss spectroscopy. The plasmon energy is 18.8±0.1 eV, the fitted quadratic dispersion coefficient is α=0.36±0.03 for 0<k<1.29 Å−1 and α L =0.52+0.04 fork<0.55 Å−1. We compare our results with the plasmon dispersion in other simple metals and point out discrepancies with the theories of the homogeneous electron gas.
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This shift is caused by the ΔE-dependent factor\(F = \left( {\left( {\frac{{\Delta {\rm E}}}{{2E_0 }}} \right.} \right)^2 + \left. {\left( {\frac{{\Delta k}}{{k_0 }}} \right)^2 } \right)^{ - 1}\) of the loss probability which is proportional toF Im\(\left( {\frac{1}{\varepsilon }} \right)\) where ΔE is the energy loss,E 0=30 keV, Δk=0.05 Å−1 andk 0 the wavenumber of the incident electrons. The influence of this factor becomes noticable for relatively large halfwidths of the plasmon lines, see Fig. 1
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Diekmann, W., Eickmans, J. & Otto, A. Plasmon dispersion in Beryllium. Z. Physik B - Condensed Matter 65, 39–41 (1986). https://doi.org/10.1007/BF01308397
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DOI: https://doi.org/10.1007/BF01308397